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It's not enough to execute systemctl daemon-reload (according to its manpage), as it only reloads systemctl's configuration but running services remain untouched. However, I recognized that executing systemctl restart docker seems to be sufficient to make dockerd listen on the TCP port.

An another note: At least for 16.04, the service description (docker.service) already takes the DOCKER_OPTS defined in /etc/default/docker into account. It's therefore not necessary to change /lib/systemd/system/docker.service